9、数据结构与算法：数组、区间与图的深入解析

数据结构与算法：数组、区间与图的深入解析

1. 数组与Fenwick树

1.1 Fenwick树的实现

Fenwick树是一种用于高效处理前缀和与区间和查询的数据结构。以下是其Python实现：

class Fenwick:
    def __init__(self, t):
        self.s = [0] * (len(t) + 1)
        # create internal storage
        for a, v in enumerate(t):
            self.add(a, v)
            # initialize

    def prefixSum(self, a):
        i = a + 1
        # internal index starts at 1
        total = 0
        while i > 0:
            # loops over neighbors
            total += self.s[i]
            # cumulative sum
            i -= (i & -i)
            # left neighbor
        return total

    def intervalSum(self, a, b):
        return self.prefixSum(b) - self.prefixSum(a - 1)

    def add(self, a, val):